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alexandr402 [8]
3 years ago
15

Renee wants to put a fence around her

Mathematics
1 answer:
kramer3 years ago
3 0

Answer:

perimeter = 322.5 ft ( to the nearest tenth of a foot)

Step-by-step explanation:

Length the length of the sides of the square be L

Area of a square = L²

∴ 6,500 = L²

L = √(6,500)

L = 80.6226

Next Let us calculate the perimeter

Perimeter of a square = L + L + L + L = 4L

perimeter = 4 × 80.6226

Perimeter = 322.4904 ft

perimeter = 322.5 ft ( to the nearest tenth of a foot)

<em>N:B rounding to the nearest tenth of a foot is same as rounding to 1 decimal place.</em>

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A rectangle has its base on the x axis and its upper two vertices on the parabola y = 9 − x2. (a) Draw a graph of this problem.
gtnhenbr [62]

Answer:

  • (a) see attached
  • (b) width: 2x; height: y = 9-x²
  • (c) A=2x(9-x²) . . . 0 ≤ x ≤ 3
  • (d) dA/dx = -6x² +18; x=±√3
  • (e) 12√3 units²

Step-by-step explanation:

(a) The attachment shows the graph of the parabola in blue. It also shows an inscribed rectangle in black.

(b) The upper right point of the rectangle is shown in the attachment as (x, y). The dimension y is the height of the rectangle. The x-dimension is half the width of the rectangle, which is symmetrical about the y-axis. Hence the width is 2x.

(c) As with any rectangle, the area is the product of length and width:

... A = (2x)(9 -x²) . . . . . the attachment shows a graph of this

... A = -2x³ +18x . . . . . expanded form suitable for differentiation

A suitable domain for A is where both x and A are non-negative: 0 ≤ x ≤ 3.

(d) The derivative of A with respect to x is ...

... A' = -6x² +18

This is defined everywhere, so the critical values will be where A' = 0.

... 0 = -6x² +18

... 3 = x² . . . . . . . divide by -6, add 3

... √3 = x . . . . . . . -√3 is also a solution, but is not in the domain of A

(e) The rectangle will have its largest area where x=√3. That area is ...

... A = 2x(9 -x²) = 2√3(9 -(√3)²) = 2√3(6)

... A = 12√3 . . . . square units . . . . ≈ 20.785 units²

7 0
3 years ago
6.5÷1345? please make the answer as short as posible.
solong [7]
6.5 ÷ 1345 = 0.0048 or 13/2690
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3 years ago
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